Title: Increasing the power of Honest Verifier Quantum Statistical Zero Knowledge proof systems
Speaker: Iordanis Kerenidis, CNRS- Univ Paris
Date: Wednesday, March 12, 2008 11:00-12:00pm
Location: DIMACS Center, CoRE Bldg, Room 431, Rutgers University, Busch Campus, Piscataway, NJ
In quantum Zero Knowledge, the assumption was made that the Verifier is only using unitary operations. Under this restriction, many nice properties have been shown about quantum Zero Knowledge, including the fact that Honest-Verifier Quantum Statistical Zero Knowledge (HVQSZK) is equal to Cheating-Verifier Quantum Statistical Zero Knowledge (QSZK).
In this talk we investigate what happens when we raise the restriction of unitarity in quantum Zero Knowledge, i.e. we allow the Verifier to apply any general quantum operation during the protocol. First, in the honest verifier case we show a striking result: any classical Interactive Proof has an Honest-Verifier Quantum Statistical Zero Knowledge proof. Note that in the classical case, honest verifier SZK is no more powerful than SZK and hence it is not believed to contain even NP. Second, if we allow a cheating verifier, then Quantum Statistical Zero Knowledge with non-unitaries is equal to Quantum Zero-Knowledge with unitaries.
One can think of our results in two complementary ways. If we would like to use the honest verifier model as a means to study the general model by taking advantage of their equivalence, then it is imperative to use the unitary definition, since with the general one this equivalence is most probably not true. On the other hand, if we would like to use quantum Zero Knowledge protocols in a cryptographic scenario where the honest-but-curious model is sufficient, then adding the unitary constraint severely decreases the power of quantum Zero Knowledge protocols. We remark that in order for the general definition to be meaningful, we also have to strengthen our definition of simulation.